I. Field Curvature
A fundamental problem of optics is the formation of images which are relatively flat. Substantial flatness is desired whether an image is to be recorded or viewed. In the case of recording, flatness is desired since most recording media are flat. In the case of an image which is to be viewed on a screen, flatness is desired since most screens are flat. In the case of an image which is to be directly viewed by the eye, flatness is desired so that the eye does not have to change its accommodation when scanning various parts of an image.
To a first approximation, the shape of the image produced by a lens system can be expressed in terms of the system's Petzval curvature (PC) given by: EQU PC=-.SIGMA.(n'-n)c.sub.b /nn' (1)
where the summation is taken over all surfaces within the system and for each surface, n is the index of refraction on the object side of the surface, n' is the index of refraction on the image side of the surface, and c.sub.b is the base curvature of the surface, c.sub.b being positive if the center of curvature is on the image side of the surface. In the case of a single lens element, PC is negative if the element is positive, and PC is positive if the element is negative.
In the past, three basic techniques have been employed to produce flat images for positive lens systems or for positive lens units within a lens system where field curvature control on unit-by-unit basis is desired:
(1) the use of matched pairs of surface radii, with element thicknesses being used to achieve a net positive optical power; PA1 (2) the use of separated negative and positive surface powers so that paraxial rays strike the surfaces with negative powers at lower heights than the heights at which they strike surfaces with positive powers, e.g., the use of a separated field flattener having a negative power; and PA1 (3) the use of combinations of positive and negative lens elements, where the positive elements have higher indices of refraction than the negative elements. PA1 (1) a large eye relief distance, e.g., about 20 mm, to allow for comfortable viewing by people with various facial characteristics and, also, those wearing glasses; PA1 (2) a large exit pupil/aperture stop diameter to allow for viewing in low light situations; PA1 (3) a large apparent total field of view, preferably 60.degree. or larger, especially in the case of VR applications; PA1 (4) a good correction of distortion and a high image quality across the system's field of view; and PA1 (5) a field curvature correction which substantially eliminates the need for reaccommodation as the user's eye scans across the image. PA1 (a) designing the system by selecting the shape of one or more aspherical surfaces in the system by determining an EFC value for the system for at least one principal ray, e.g., by using the EFC parameter or an equivalent parameter (see below) as a criterium for obtaining an appropriate shape for an aspherical surface; and PA1 (b) producing the lens system designed in step (a). PA1 a positive objective lens unit (first lens unit) which forms an intermediate image of the object, has an exit pupil, and includes at least one power element and at least one FCC; and PA1 an eyepiece lens unit (second lens unit) which reimages the intermediate image to form the image of the object, said unit having an entrance pupil.
Combinations of these techniques have also been used.
In the case of a negative lens system or a negative lens unit, only two approaches have been known, namely, the use of a positive field flattener, which is only applicable where a short image distance is permissible, and the use of combinations of positive and negative lens elements, where the negative elements have higher indices of refraction than the positive elements, i.e., the last of the three approaches available for positive lens systems with the indices reversed.
These approaches to achieving relatively flat images have often suffered from problems of increased complexity and cost of the overall lens system. Complexity is often increased because as elements are added, e.g., a field flattener, additional compensating elements also must often be added to achieve the desired total power of the system. Moreover, as these additional elements are added, aberration correction becomes more difficult, which, in turn, may lead to more complexity. Cost is often increased due to increased complexity and because more expensive materials are used to obtain the required indices of refraction.
In some cases, a field flattener can be used without adding additional compensating elements, e.g., when the field flattener is near to the image or object plane. However, this approach is not usually viable when there are exit pupil position requirements at the image plane, e.g., in the case of an intermediate image or a telecentric image or object.
Notwithstanding these well-known drawbacks, prior to the present invention, only the foregoing approaches were known for controlling field curvature.
II. Magnifiers
Magnifiers comprise one of the most widely used and most basic optical systems known in the art. In addition to their numerous historical uses, magnifiers have recently become of central importance in the development of virtual reality (VR) viewing systems. Accordingly, the present invention is illustrated by means of magnifier systems and, in particular, magnifier systems suitable for use in forming virtual reality images, it being understood that the use of these systems for purposes of illustration is not in anyway intended to limit the scope of the invention.
Field curvature is of particular importance in VR viewing systems because such systems are generally designed to provide a wide field of view which the user is expected to view over an extended period of time. Accordingly, a magnifier with substantial field curvature is not suitable for such a system since the user's eyes are likely to tire rapidly if substantial reaccommodation is needed to view different parts of the VR image.
In its most simple form, a magnifier can be a single positive element with an external stop coincident with the position of the observer's eye. In this form, magnifiers can achieve magnifications on the order of 2X to 4X and can provide a small field of view over which the image quality is acceptable.
For more critical applications, such as, the detailed visual inspection of a small object or the viewing of an imaging display (e.g., an electroluminescent, CRT, or LCD display), a color correcting doublet may be added. Large negative Petzval curvature and lateral color, however, still remain, thus limiting the total field over which a reasonably high image quality can be achieved to about 40.degree..
Historically, correction of the Petzval curvature of a magnifier has typically involved the addition of a negative element, i.e., approach (2) above. However, as discussed above, adding a negative element requires the addition of more positive power, leading to a more complicated system. As a result, when a magnifier having a larger field of view and/or a better image quality is required, e.g., a microfiche loupe, the number of elements is often 5 or 6, and, even then, field curvature and lateral color cause the image to degrade at full field.
Betensky, U.S. Pat. No. 4,094,585, and Loy, U.S. Pat. No. 4,679,912, disclose lens systems designed to provide a wide field of view without the use of a large number of lens elements. In practice, the systems of these patents turn out to be difficult to manufacture.
Thus, the Betensky patent discloses a three element form consisting of a single positive element and a cemented doublet concave to the object. Field curvature is corrected by incorporating a strong negative element in the doublet which makes a positive contribution to the Petzval sum and by having the doublet be in the form of a thick meniscus lens concave to the object. Lateral color is corrected by having a very strong interface between the positive and the negative elements of the doublet. The doublet includes either an aspherical interface or aspherical outer surfaces.
In practice, the problem of cementing together two pieces of plastic material with high thermal expansion coefficients without generating large residual internal stresses has prevented this design from becoming a commonly used one.
The Loy patent provides a flat field by first imaging the object onto a curved surface concave to the viewer by means of a fiber optics image guide. This approach allows for fewer lens elements, but the fiber optics device which it requires is expensive, and the use of such devices in large commercial volumes is not feasible with present technology.